Space of modular forms of level 243, weight 2, and Character 243.i

• Label: 243.2.i
• Level: $243$
• Weight: $2$
• Character orbit: 243.i
• Rep. character: $\chi_{243}(4,\cdot)$
• Character field: $\Q(\zeta_{81})$
• Dimension: $1404$
• Newform subspaces: $1$
• Sturm bound: $54$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.i (of order \(81\) and degree \(54\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 243 \)
Character field:			\(\Q(\zeta_{81})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(54\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(243, [\chi])\).

	Total	New	Old
Modular forms	1512	1512	0
Cusp forms	1404	1404	0
Eisenstein series	108	108	0

Trace form

\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(243, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
243.2.i.a	$243$	$2$	243.i	243.i	$81$	$1404$	$26$	$1.940$		None		$2$	$0$	\(-54\)	\(-54\)	\(-54\)	\(-54\)		$\mathrm{SU}(2)[C_{81}]$